import numpy as np

a = np.array([[0.3, 0.1, 0.1],
              [0.1, 0.3, -0.1],
              [0.1, -0.1, 0.3]])

b = np.linalg.inv(a)
c = np.matmul(b, np.array([[-0.5, -0.5, -0.5]]).T)
print(c)